Simplify the following expression: $p = \dfrac{7}{42n - 7}$ You can assume $n \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $7 = (7)$ The denominator can be factored: $42n - 7 = (2\cdot3\cdot7 \cdot n) - (7)$ The greatest common factor of all the terms is $7$ Factoring out $7$ gives us: $p = \dfrac{(7)(1)}{(7)(6n - 1)}$ Dividing both the numerator and denominator by $7$ gives: $p = \dfrac{1}{6n - 1}$